Finite Group Databasebeta

← C2×#22597413 #32862232

Subgroups — C2×#22597413 #32862232

Order 18176.

2230 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986545C211yesmaximal, characteristic
2#22597413C2116yesmaximal, direct product factor
3C2×#17986075C211yesmaximal, characteristic, complemented
4C2×#17986074C211yesmaximal, characteristic, complemented
5C2×#17986073C211yesmaximal, characteristic, complemented
6C2×#17986070C211yesmaximal, characteristic, complemented
7C2×#17986068C211yesmaximal, characteristic, complemented
8C2×#17986067C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D71C211yesmaximal, characteristic, complemented
10C2×(C22⋊D71)⋊C8C211yesmaximal, characteristic, complemented
11C2×#17986053C211yesmaximal, characteristic, complemented
12C2×#17986049C211yesmaximal, characteristic, complemented
13C2×#17985966C211yesmaximal, characteristic, complemented
14C2×#17985964C211yesmaximal, characteristic, complemented
15C2×#17985964C211yesmaximal, characteristic, complemented
16C2×#408×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19C22×#11765848C2211yescharacteristic
20C22×#11765848C2211yescharacteristic
21C23×C71⋊C8C2211yescharacteristic
22C22×C8×D71C2211yescharacteristic
23C22×C8×D71C2211yescharacteristic
24#17986545C418yes—
25#17986545C2218yes—
26C2×#14556126C411yescharacteristic
27C2×#14556124C411yescharacteristic
28C2×#14556117C411yescharacteristic
29C2×#14556115C411yescharacteristic
30C2×#14556100C411yescharacteristic
31C2×#14556100C411yescharacteristic
32C2×#14556100C411yescharacteristic
33C2×#14556100C411yescharacteristic
34C2×C4×C22⋊D71C2211yescharacteristic
35C2×C4×C22⋊D71C2211yescharacteristic
36C2×C4×C22⋊D71C2211yescharacteristic
37C2×C4×C22⋊D71C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39#17986075C2218yescomplemented
40#17986074C2218yescomplemented
41#17986073C2218yescomplemented
42#17986070C2218yescomplemented
43#17986068C2218yescomplemented
44#17986067C2218yescomplemented
45C8×C22⋊D71C2218yescomplemented
46(C22⋊D71)⋊C8C2218yescomplemented
47#17986053C2218yescomplemented
48#17986049C2218yescomplemented
49C2×Dic71⋊C8C2211yescharacteristic
50C2×Dic71⋊C8C2211yescharacteristic
51C2×Dic71⋊C8C2211yescharacteristic
52C2×Dic71⋊C8C2211yescharacteristic
53#17985966C2218yescomplemented
54#17985964C2218yescomplemented
55#17985964C2218yescomplemented
56C2×C22⋊(C71⋊C8)C2211yescharacteristic
57C2×C22⋊(C71⋊C8)C2211yescharacteristic
58C2×C22⋊(C71⋊C8)C2211yescharacteristic
59C2×C22⋊(C71⋊C8)C2211yescharacteristic
60C2×(C2×D71)⋊C8C2211yescharacteristic
61C2×(C2×D71)⋊C8C2211yescharacteristic
62C2×(C2×D71)⋊C8C2211yescharacteristic
63C2×(C2×D71)⋊C8C2211yescharacteristic
64C2×#14556038C2211yescharacteristic
65C2×#14556038C2211yescharacteristic
66C2×C8×Dic71C2211yescharacteristic
67C2×C8×Dic71C2211yescharacteristic
68C22×#41×C71C2211yescharacteristic
69C22×M16×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71#408×C71C2218yescomplemented
72C2×C22⋊C8×C71C2211yescharacteristic
73C2×C22⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic
76C2×#11765865—42no—
77C2×#11765865—42no—
78C2×#11765865C2×C414yes—
79C2×#11765865C2314yes—
80C22×Dic142C2×C411yescharacteristic
81C22×D284C2×C411yescharacteristic
82C22×C22⋊D71C2×C411yescharacteristic
83C22×C22⋊D71C2×C411yescharacteristic
84C22×C22⋊D71C2×C411yescharacteristic
85C22×C22⋊D71C2×C411yescharacteristic
86C22×C22⋊D71C2×C411yescharacteristic
87C22×C22⋊D71C2×C411yescharacteristic
88C23×Dic71C2×C411yescharacteristic
89C23×Dic71C2×C411yescharacteristic
90C22×C4×D71C2311yescharacteristic
91C22×C4×D71C2311yescharacteristic
92C2×#11765849—42no—
93C2×#11765849C2314yes—
94C2×#11765848—42no—
95C2×#11765848—42no—
96C2×#11765848C2314yes—
97C2×#11765848C2314yes—
98C22×C71⋊C8—42no—
99C22×C71⋊C8C2311yescharacteristic
100C22×C71⋊C8C2311yescharacteristic
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2311yescharacteristic
103C22×C71⋊C8C2314yes—
104C2×C8×D71—42no—
105C2×C8×D71—42no—
106C2×C8×D71C2314yes—
107C2×C8×D71C2314yes—
108#14556126C2×C418yes—
109#14556124C2×C418yes—
110#14556117C2×C418yes—
111#14556115C2×C418yes—
112#14556100C2×C418yes—
113#14556100C2×C418yes—
114#14556100C2×C418yes—
115#14556100C2×C418yes—
116C4×C22⋊D71C2×C414yes—
117C4×C22⋊D71C2×C414yes—
118C4×C22⋊D71C2×C414yes—
119C4×C22⋊D71C2×C414yes—
120C4×C22⋊D71C2314yes—
121C4×C22⋊D71C2314yes—
122C4×C22⋊D71C2314yes—
123C4×C22⋊D71C2314yes—
124C2×Dic71⋊C4C2×C411yescharacteristic
125C2×Dic71⋊C4C2×C411yescharacteristic
126C2×Dic71⋊C4C2×C411yescharacteristic
127C2×Dic71⋊C4C2×C411yescharacteristic
128C2×C22⋊Dic71C2×C411yescharacteristic
129C2×C22⋊Dic71C2×C411yescharacteristic
130C2×C22⋊Dic71C2×C411yescharacteristic
131C2×C22⋊Dic71C2×C411yescharacteristic
132C2×(C2×D71)⋊C4C2×C411yescharacteristic
133C2×(C2×D71)⋊C4C2×C411yescharacteristic
134C2×(C2×D71)⋊C4C2×C411yescharacteristic
135C2×(C2×D71)⋊C4C2×C411yescharacteristic
136C2×C4×Dic71C2×C411yescharacteristic
137C2×C4×Dic71C2×C411yescharacteristic
138C2×C4×Dic71C2×C414yes—
139C2×C4×Dic71C2314yes—
140C2×C4×Dic71C2311yescharacteristic
141C2×C4×Dic71C2311yescharacteristic
142Dic71⋊C8C2314yes—
143Dic71⋊C8C2314yes—
144Dic71⋊C8C2314yes—
145Dic71⋊C8C2314yes—
146C22⋊(C71⋊C8)C2314yes—
147C22⋊(C71⋊C8)C2314yes—
148C22⋊(C71⋊C8)C2314yes—
149C22⋊(C71⋊C8)C2314yes—
150(C2×D71)⋊C8C2314yes—
151(C2×D71)⋊C8C2314yes—
152(C2×D71)⋊C8C2314yes—
153(C2×D71)⋊C8C2314yes—
154#14556038C2314yes—
155#14556038C2314yes—
156C8×Dic71C2314yes—
157C8×Dic71C2314yes—
158C2×#41×C71—42no—
159C2×#41×C71—42no—
160C2×#41×C71C2×C414yes—
161C2×#41×C71C2314yes—
162C22×Q8×C71C2×C411yescharacteristic
163C22×D4×C71C2×C411yescharacteristic
164C22×D4×C71C2×C411yescharacteristic
165C22×D4×C71C2×C411yescharacteristic
166C23×C4×C71C2311yescharacteristic
167C23×C4×C71C2311yescharacteristic
168C23×C4×C71C2311yescharacteristic
169C2×M16×C71—42no—
170C2×M16×C71C2314yes—
171C22×C8×C71—42no—
172C22×C8×C71C2311yescharacteristic
173C22×C8×C71C2311yescharacteristic
174C22×C8×C71C2311yescharacteristic
175C22×C8×C71C2311yescharacteristic
176C22×C8×C71C2314yes—
177C22⋊C8×C71C2314yes—
178C22⋊C8×C71C2314yes—
179C22⋊C8×C71C2314yes—
180C22⋊C8×C71C2314yes—
181C23×D71C22×C411yescharacteristic
182C23×D71C22×C411yescharacteristic
183#11765865—48no—
184#11765865—44no—
185#11765865—44no—
186C2×Dic142—42no—
187C2×Dic142C22×C414yes—
188C2×D284—42no—
189C2×D284C22×C414yes—
190C2×C22⋊D71—24no—
191C2×C22⋊D71—24no—
192C2×C22⋊D71—42no—
193C2×C22⋊D71—42no—
194C2×C22⋊D71—42no—
195C2×C22⋊D71—42no—
196C2×C22⋊D71C22×C414yes—
197C2×C22⋊D71C22×C414yes—
198C2×C22⋊D71C22×C414yes—
199C2×C22⋊D71C22×C414yes—
200C2×C22⋊D71C22×C414yes—
201C2×C22⋊D71C22×C414yes—
202C22×Dic71—24no—
203C22×Dic71—42no—
204C22×Dic71C22×C411yescharacteristic
205C22×Dic71C22×C411yescharacteristic
206C22×Dic71C22×C411yescharacteristic
207C22×Dic71C22×C411yescharacteristic
208C22×Dic71C22×C411yescharacteristic
209C22×Dic71C22×C414yes—
210C22×Dic71C22×C414yes—
211C22×Dic71C22×C411yescharacteristic
212C2×C4×D71—22no—
213C2×C4×D71—22no—
214C2×C4×D71—22no—
215C2×C4×D71—22no—
216C2×C4×D71C22×C412yes—
217C2×C4×D71C22×C412yes—
218C2×C4×D71C2412yes—
219C2×C4×D71C2412yes—
220#11765849—44no—
221#11765848—44no—
222#11765848—44no—
223C2×C71⋊C8—22no—
224C2×C71⋊C8—22no—
225C2×C71⋊C8—22no—
226C2×C71⋊C8—22no—
227C2×C71⋊C8—44no—
228C2×C71⋊C8C2412yes—
229C2×C71⋊C8C2412yes—
230C2×C71⋊C8C2412yes—
231C2×C71⋊C8C2412yes—
232C8×D71—44no—
233C8×D71—44no—
234Dic71⋊C4C22×C414yes—
235Dic71⋊C4C22×C414yes—
236Dic71⋊C4C22×C414yes—
237Dic71⋊C4C22×C414yes—
238C22⋊Dic71C22×C414yes—
239C22⋊Dic71C22×C414yes—
240C22⋊Dic71C22×C414yes—
241C22⋊Dic71C22×C414yes—
242(C2×D71)⋊C4C22×C414yes—
243(C2×D71)⋊C4C22×C414yes—
244(C2×D71)⋊C4C22×C414yes—
245(C2×D71)⋊C4C22×C414yes—
246C4×Dic71C22×C412yes—
247C4×Dic71C22×C412yes—
248C4×Dic71C22×C414yes—
249C4×Dic71C22×C414yes—
250C4×Dic71C2412yes—
251C4×Dic71C2412yes—
252C24×C71C22×C411yescharacteristic
253C24×C71C22×C411yescharacteristic
254C24×C71C22×C411yescharacteristic
255#41×C71—48no—
256#41×C71—44no—
257#41×C71—44no—
258C2×Q8×C71—42no—
259C2×Q8×C71C22×C414yes—
260C2×D4×C71—42no—
261C2×D4×C71—42no—
262C2×D4×C71—42no—
263C2×D4×C71C22×C414yes—
264C2×D4×C71C22×C414yes—
265C2×D4×C71C22×C414yes—
266C22×C4×C71—22no—
267C22×C4×C71—22no—
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71—22no—
271C22×C4×C71—22no—
272C22×C4×C71C22×C411yescharacteristic
273C22×C4×C71C22×C412yes—
274C22×C4×C71C22×C411yescharacteristic
275C22×C4×C71C22×C411yescharacteristic
276C22×C4×C71C22×C412yes—
277C22×C4×C71C22×C412yes—
278C22×C4×C71C2412yes—
279C22×C4×C71C2412yes—
280C22×C4×C71C2412yes—
281C22×C4×C71C2411yescharacteristic
282M16×C71—44no—
283C2×C8×C71—22no—
284C2×C8×C71—22no—
285C2×C8×C71—22no—
286C2×C8×C71—22no—
287C2×C8×C71—44no—
288C2×C8×C71C2412yes—
289C2×C8×C71C2412yes—
290C2×C8×C71C2412yes—
291C2×C8×C71C2412yes—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—22no—
300C23×C71—22no—
301C23×C71C23×C412yes—
302C23×C71C23×C412yes—
303C23×C71C23×C412yes—
304C23×C71C23×C411yescharacteristic
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—22no—
308C22×D71—22no—
309C22×D71—22no—
310C22×D71—22no—
311C22×D71C23×C412yes—
312C22×D71C23×C412yes—
313Q8×C71—44no—
314D4×C71—44no—
315D4×C71—44no—
316D4×C71—44no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—24no—
321C2×C4×C71—24no—
322C2×C4×C71—24no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71C23×C412yes—
330C2×C4×C71C23×C412yes—
331C2×C4×C71C23×C412yes—
332C2×C4×C71C23×C411yescharacteristic
333C2×C4×C71H(5,𝔽2)12yes—
334C2×C4×C71H(5,𝔽2)12yes—
335C2×C4×C71C2511yescharacteristic
336C22⋊D71—28no—
337C22⋊D71—28no—
338C22⋊D71—44no—
339C22⋊D71—44no—
340C22⋊D71—44no—
341C22⋊D71—44no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—28no—
348C2×Dic71—44no—
349C2×Dic71#13114yes—
350C2×Dic71C23×C412yes—
351C2×Dic71C23×C412yes—
352C2×Dic71C23×C412yes—
353C2×Dic71C23×C412yes—
354C2×Dic71C23×C412yes—
355C2×Dic71C23×C412yes—
356D284—44no—
357C4×D71—24no—
358C4×D71—24no—
359C4×D71—22no—
360C4×D71—22no—
361C4×D71—22no—
362C4×D71—22no—
363Dic142—44no—
364C8×C71—22no—
365C8×C71—22no—
366C8×C71—22no—
367C8×C71—22no—
368C71⋊C8—22no—
369C71⋊C8—22no—
370C71⋊C8—22no—
371C71⋊C8—22no—
372C22×C71—22no—
373C22×C71—22no—
374C22×C71—22no—
375C22×C71—22no—
376C22×C71—22no—
377C22×C71—22no—
378C22×C71—22no—
379C22×C71—22no—
380C22×C71—22no—
381C22×C71—44no—
382C22×C71—44no—
383C22×C71—44no—
384C22×C71#51812yes—
385C22×C71C2×#13112yes—
386C22×C71#56812yes—
387C22×C71C24×C411yescharacteristic
388C2×D71—22no—
389C2×D71—22no—
390C2×D71—22no—
391C2×D71—22no—
392C2×D71—22no—
393C2×D71—22no—
394C2×D71—44no—
395C2×D71—44no—
396C4×C71—22no—
397C4×C71—22no—
398C4×C71—22no—
399C4×C71#51812yes—
400C4×C71C2×H(5,𝔽2)11yescharacteristic
401C4×C71C2×H(5,𝔽2)11yescharacteristic
402Dic71—22no—
403Dic71—22no—
404Dic71—22no—
405Dic71—22no—
406Dic71—22no—
407Dic71C2×#13114yes—
408C2×#2981—711nomaximal, Sylow
409C2×C71—42no—
410C2×C71—42no—
411C2×C71—42no—
412C2×C71#298114yescomplemented
413C2×C71C2×#51811yescharacteristic
414C2×C71C22×#13111yescharacteristic
415C2×C71C2×#56811yescharacteristic
416D71—42no—
417D71—42no—
418C2×#532—711no—
419#2981—7116no—
420C2×#436—711no—
421C2×#436—711no—
422C2×#435—711no—
423C2×#435—711no—
424C2×#435—711no—
425C2×#435—711no—
426C2×C8×D4—711no—
427C2×C8×D4—711no—
428C2×#432—711no—
429C2×#431—711no—
430C2×#408—711no—
431C2×#408—711no—
432C2×#408—711no—
433C2×#408D7111yescharacteristic, complemented
434C71C2×#298111yescharacteristic, complemented, Sylow
435C22×#41—711no—
436C22×#41C2×D7111yescharacteristic
437C22×M16—711no—
438C22×M16—711no—
439C22×M16—711no—
440C22×M16C2×D7111yescharacteristic
441C23×C8—711no—
442C23×C8—711no—
443C23×C8—711no—
444C23×C8C2×D7111yescharacteristic
445#532—718no—
446#532—718no—
447C2×C4⋊Q8—711no—
448C2×#127—711no—
449C2×#124—711no—
450C2×#124—711no—
451C2×#121—711no—
452C2×#121—711no—
453C2×#121—711no—
454C2×#121—711no—
455C2×C4×D4—711no—
456C2×C4×D4—711no—
457C2×C4×D4—711no—
458C2×C4×D4—711no—
459C22×C42—711no—
460#436—718no—
461#436—718no—
462#435—718no—
463#435—718no—
464#435—718no—
465#435—718no—
466C8×D4—718no—
467C8×D4—718no—
468#432—718no—
469#431—718no—
470C2×C4⋊C8—711no—
471C2×C4⋊C8—711no—
472C2×C4⋊C8—711no—
473C2×C4⋊C8—711no—
474#408—718no—
475#408—718no—
476#408—718no—
477#408C2×D7118yescomplemented
478C2×C22⋊C8—711no—
479C2×C22⋊C8—711no—
480C2×C22⋊C8—711no—
481C2×C22⋊C8—711no—
482C2×C22⋊C8—711no—
483C2×C22⋊C8—711no—
484C2×C22⋊C8—711no—
485C2×C22⋊C8—711no—
486C2×C22⋊C8C2×D7111yescharacteristic
487C2×C22⋊C8C2×D7111yescharacteristic
488C2×C22⋊C8C2×D7111yescharacteristic
489C2×C22⋊C8C2×D7111yescharacteristic
490C2×#97—711no—
491C2×#97—711no—
492C2×C4×C8—711no—
493C2×C4×C8—711no—
494C2×#41—42no—
495C2×#41—42no—
496C2×#41—2842no—
497C2×#41—2842no—
498C2×#41—714no—
499C2×#41—714no—
500C2×#41C4×D7114yes—
501C2×#41C22×D7114yes—
502C22×Q8—711no—
503C22×Q8C4×D7111yescharacteristic
504C22×D4—711no—
505C22×D4—711no—
506C22×D4—711no—
507C22×D4—711no—
508C22×D4—711no—
509C22×D4—711no—
510C22×D4—711no—
511C22×D4C4×D7111yescharacteristic
512C22×D4C4×D7111yescharacteristic
513C22×D4C4×D7111yescharacteristic
514C23×C4—711no—
515C23×C4—711no—
516C23×C4—711no—
517C23×C4—711no—
518C23×C4C22×D7111yescharacteristic
519C23×C4C22×D7111yescharacteristic
520C23×C4C22×D7111yescharacteristic
521C2×M16—42no—
522C2×M16—2842no—
523C2×M16—2842no—
524C2×M16—2842no—
525C2×M16—714no—
526C2×M16—714no—
527C2×M16—714no—
528C2×M16C22×D7114yes—
529C22×C8—42no—
530C22×C8—2842no—
531C22×C8—2842no—
532C22×C8—2842no—
533C22×C8—714no—
534C22×C8—714no—
535C22×C8—714no—
536C22×C8—711no—
537C22×C8—711no—
538C22×C8—711no—
539C22×C8—711no—
540C22×C8C22×D7111yescharacteristic
541C22×C8C22×D7111yescharacteristic
542C22×C8C22×D7111yescharacteristic
543C22×C8C22×D7111yescharacteristic
544C22×C8C22×D7114yes—
545C4⋊Q8—718no—
546#127—718no—
547#124—718no—
548#124—718no—
549#121—718no—
550#121—718no—
551#121—718no—
552#121—718no—
553C4×D4—714no—
554C4×D4—714no—
555C4×D4—714no—
556C4×D4—714no—
557C4×D4—714no—
558C4×D4—714no—
559C4×D4—714no—
560C4×D4—714no—
561C2×C4⋊C4—711no—
562C2×C4⋊C4—711no—
563C2×C4⋊C4—711no—
564C2×C4⋊C4—711no—
565C2×C22⋊C4—711no—
566C2×C22⋊C4—711no—
567C2×C22⋊C4—711no—
568C2×C22⋊C4—711no—
569C2×C22⋊C4—711no—
570C2×C22⋊C4—711no—
571C2×C22⋊C4—711no—
572C2×C22⋊C4—711no—
573C2×C42—711no—
574C2×C42—711no—
575C2×C42—714no—
576C2×C42—714no—
577C2×C42—711no—
578C2×C42—711no—
579C4⋊C8—714no—
580C4⋊C8—714no—
581C4⋊C8—714no—
582C4⋊C8—714no—
583C22⋊C8—714no—
584C22⋊C8—714no—
585C22⋊C8—714no—
586C22⋊C8—714no—
587C22⋊C8—714no—
588C22⋊C8—714no—
589C22⋊C8—714no—
590C22⋊C8—714no—
591C22⋊C8C22×D7114yes—
592C22⋊C8C22×D7114yes—
593C22⋊C8C22×D7114yes—
594C22⋊C8C22×D7114yes—
595#97—714no—
596#97—714no—
597C4×C8—714no—
598C4×C8—714no—
599C24—711no—
600C24—711no—
601C24C2×C4×D7111yescharacteristic
602C24C2×C4×D7111yescharacteristic
603C24C2×C4×D7111yescharacteristic
604#41—48no—
605#41—44no—
606#41—44no—
607#41—2844no—
608#41—2844no—
609#41—2848no—
610C2×Q8—42no—
611C2×Q8—2842no—
612C2×Q8—714no—
613C2×Q8C2×C4×D7114yes—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—2842no—
618C2×D4—2842no—
619C2×D4—2842no—
620C2×D4—2842no—
621C2×D4—2842no—
622C2×D4—714no—
623C2×D4—714no—
624C2×D4—714no—
625C2×D4—714no—
626C2×D4—714no—
627C2×D4—714no—
628C2×D4—714no—
629C2×D4—1424no—
630C2×D4—1424no—
631C2×D4C2×C4×D7114yes—
632C2×D4C2×C4×D7114yes—
633C2×D4C2×C4×D7114yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—2842no—
641C22×C4—714no—
642C22×C4—711no—
643C22×C4—711no—
644C22×C4—711no—
645C22×C4—711no—
646C22×C4—714no—
647C22×C4—711no—
648C22×C4—711no—
649C22×C4—712no—
650C22×C4—712no—
651C22×C4—712no—
652C22×C4—712no—
653C22×C4—1424no—
654C22×C4—1422no—
655C22×C4—1422no—
656C22×C4—1422no—
657C22×C4—1422no—
658C22×C4C2×C4×D7111yescharacteristic
659C22×C4C2×C4×D7112yes—
660C22×C4C2×C4×D7111yescharacteristic
661C22×C4C2×C4×D7111yescharacteristic
662C22×C4C2×C4×D7112yes—
663C22×C4C2×C4×D7112yes—
664C22×C4C23×D7112yes—
665C22×C4C23×D7112yes—
666C22×C4C23×D7112yes—
667C22×C4C23×D7111yescharacteristic
668M16—44no—
669M16—2844no—
670M16—2844no—
671M16—2844no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—2844no—
678C2×C8—2844no—
679C2×C8—2844no—
680C2×C8—712no—
681C2×C8—712no—
682C2×C8—712no—
683C2×C8—712no—
684C2×C8—1422no—
685C2×C8—1422no—
686C2×C8—1422no—
687C2×C8—1422no—
688C2×C8C23×D7112yes—
689C2×C8C23×D7112yes—
690C2×C8C23×D7112yes—
691C2×C8C23×D7112yes—
692C4⋊C4—714no—
693C4⋊C4—714no—
694C4⋊C4—714no—
695C4⋊C4—714no—
696C22⋊C4—714no—
697C22⋊C4—714no—
698C22⋊C4—714no—
699C22⋊C4—714no—
700C22⋊C4—714no—
701C22⋊C4—714no—
702C22⋊C4—714no—
703C22⋊C4—714no—
704C42—712no—
705C42—712no—
706C42—714no—
707C42—714no—
708C42—712no—
709C42—712no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—712no—
720C23—712no—
721C23—1422no—
722C23—1422no—
723C23—1422no—
724C23—1422no—
725C23—1422no—
726C23—1422no—
727C23C22×C4×D7112yes—
728C23C22×C4×D7112yes—
729C23C22×C4×D7112yes—
730C23C22×C4×D7111yescharacteristic
731Q8—44no—
732Q8—2844no—
733D4—44no—
734D4—44no—
735D4—44no—
736D4—2844no—
737D4—2844no—
738D4—2844no—
739D4—2844no—
740D4—2844no—
741D4—1428no—
742D4—1428no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—2844no—
756C2×C4—712no—
757C2×C4—714no—
758C2×C4—712no—
759C2×C4—712no—
760C2×C4—712no—
761C2×C4—712no—
762C2×C4—712no—
763C2×C4—1428no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4—1422no—
770C2×C4—1422no—
771C2×C4—1422no—
772C2×C4—1422no—
773C2×C4—1424no—
774C2×C4—1424no—
775C2×C4C22×C4×D7112yes—
776C2×C4C22×C4×D7112yes—
777C2×C4C22×C4×D7112yes—
778C2×C4C22×C4×D7111yescharacteristic
779C2×C4#1455617312yes—
780C2×C4#1455617312yes—
781C2×C4C24×D7111yescharacteristic
782C8—22no—
783C8—22no—
784C8—22no—
785C8—22no—
786C8—1422no—
787C8—1422no—
788C8—1422no—
789C8—1422no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—2844no—
803C22—2844no—
804C22—1422no—
805C22—1422no—
806C22—1422no—
807C22—1422no—
808C22—1422no—
809C22—1422no—
810C22#1798647212yes—
811C22#131×D7112yes—
812C22#1798676412yes—
813C22C23×C4×D7111yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—714no—
818C4—1422no—
819C4—1422no—
820C4—1422no—
821C4—1422no—
822C4—1422no—
823C4#1798647212yes—
824C4C2×#1455617311yescharacteristic
825C4C2×#1455617311yescharacteristic
826C2—42no—
827C2—42no—
828C2—42no—
829C2—2842no—
830C2—2842no—
831C2#2259741314yesdirect product factor
832C2C2×#1798647211yescharacteristic
833C2C2×#131×D7111yescharacteristic
834C2C2×#1798676411yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutatorC22×C71C24×C4
FrattiniC2×C4C24×D71
FittingC2×#408×C71C2
socleC23×C71C23×C4
prime radicalC2×#17986545C2
cosocleC2×C4×C71C25
hypercenterC2×#408D71
hypocenterC71C2×#2981
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22597413C2direct (N × H)
3. C2×#17986075C2semidirect
4. C2×#17986074C2semidirect
5. C2×#17986073C2semidirect
6. C2×#17986070C2semidirect
7. C2×#17986068C2semidirect
8. C2×#17986067C2semidirect
9. C2×C8×C22⋊D71C2semidirect
10. C2×(C22⋊D71)⋊C8C2semidirect
11. C2×#17986053C2semidirect
12. C2×#17986049C2semidirect
13. C2×#17985966C2semidirect
14. C2×#17985964C2semidirect
15. C2×#17985964C2semidirect
16. C2×#408×C71C2semidirect
39. #17986075C22semidirect
40. #17986074C22semidirect
41. #17986073C22semidirect
42. #17986070C22semidirect
43. #17986068C22semidirect
44. #17986067C22semidirect
45. C8×C22⋊D71C22semidirect
46. (C22⋊D71)⋊C8C22semidirect
47. #17986053C22semidirect
48. #17986049C22semidirect
53. #17985966C22semidirect
54. #17985964C22semidirect
55. #17985964C22semidirect
71. #408×C71C22semidirect
412. C2×C71#2981semidirect
433. C2×#408D71semidirect
434. C71C2×#2981semidirect
477. #408C2×D71semidirect
831. C2#22597413direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179865452
#225974132
C2×#179860752
C2×#179860742
C2×#179860732
C2×#179860702
C2×#179860682
C2×#179860672
C2×C8×C22⋊D712
C2×(C22⋊D71)⋊C82
C2×#179860532
C2×#179860492
C2×#179859662
C2×#179859642
C2×#408×C712
C2×#298171